In the previous chapter we looked at distributed ways of meeting global constraints. Here we up the ante; we ask how agents can, in a distributed fashion, optimize a global objective function. Specifically, we consider four families of techniques and associated sample problems. They are, in order:

• distributed dynamic programming (as applied to path-planning problems);

• distributed solutions to Markov Decision Problems (MDPs);

• optimization algorithms with an economic flavor (as applied to matching and scheduling problems); and

• coordination via social laws and conventions, and the example of traffic rules.

Distributed dynamic programming for path planning

Like graph coloring, path planning constitutes another common abstract problemsolving framework. A path-planning problem consists of a weighted directed graph with a set of n nodes N, directed links L, a weight function w : L ↦ ℝ+, and two nodes s, t ∈ N. The goal is to find a directed path from s to t having minimal total weight. More generally, we consider a set of goal nodes T ⊂ N, and are interested in the shortest path from s to any of the goal nodes t ∈ T.

This abstract framework applies in many domains. Certainly it applies when there is some concrete network at hand (e.g., a transportation or telecommunication network). But it also applies in more roundabout ways.